Finite Group Databasebeta

← Prev (#44568816) Next (#44568818) →

C3×C11×#11758267 #44568817

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C7

Aliases

direct productC3×C11×#11758267

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C4
derived, HallC5×C72 ⋊ C3×C4×C11
HallC5×C72×C11 ⋊ C3×C4
HallC3×C72×C11 ⋊ Dic5
HallC3×C5×C72 ⋊ C4×C11
HallC72×C11 ⋊ C3×Dic5
HallC3×C5×C11 ⋊ #5997
HallC3×C72 ⋊ C11×Dic5
HallC5×C11 ⋊ C3×#5997
SylowC72 ⋊ C3×C11×Dic5
HallC3×C5 ⋊ C11×#5997
SylowC5 ⋊ C3×C11×#5997

Subgroups

subgroupG/H
center, hypercenterC3×C11#11758267
commutator, hypocenterC5×C72C3×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C5×C11×C7⋊D7C2
cosocleC5×C7⋊D7C2×C3×C11
LCSG ▷ C5×C72
UCSC1 ◁ C3×C11

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 519);